Subgroups — C₂×#13117065 #16018209

Order 3328.

622 conjugacy classes of subgroups.

The subgroup lattice has 216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718360	C₂	1	1	yes	maximal, characteristic
2	#13117065	C₂	1	8	yes	maximal, direct product factor
3	C₂×#11718084	C₂	1	4	yes	maximal
4	C₂×C₄×#6090	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#500	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
7	C₂²×Dic₅₂	—	2	1	no	—
8	C₂²×Dic₅₂	C₂²	1	2	yes	—
9	C₂×#88123	—	2	1	no	—
10	C₁₃×#500	—	2	2	no	—
11	C₁₃×#500	C₂²	1	4	yes	—
12	C₂×C₁₃×#107	—	2	1	no	—
13	C₂×C₁₃×#107	C₂²	1	2	yes	—
14	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂²×#6090	C₂²	1	2	yes	—
16	#11718360	—	2	2	no	—
17	#11718360	C₂²	1	4	yes	—
18	#11718084	C₂²	1	16	yes	—
19	C₄×#6090	C₂²	1	4	yes	—
20	C₂²×Q₈×C₁₃	—	4	1	no	—
21	C₂²×Dic₂₆	—	2	2	no	—
22	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
24	C₁₃×C₄⋊Q₈	—	2	4	no	—
25	C₁₃×C₄⋊Q₈	—	4	2	no	—
26	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
27	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
28	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
29	C₂×C₄⋊Dic₁₃	—	4	1	no	—
30	C₂×C₄⋊Dic₁₃	—	4	1	no	—
31	C₂×Dic₅₂	—	2	8	no	—
32	C₂×Dic₅₂	—	2	4	no	—
33	C₂×Dic₅₂	—	2	2	no	—
34	C₂×Dic₅₂	—	4	4	no	—
35	C₂×Dic₅₂	C₂³	1	4	yes	—
36	#88123	—	2	4	no	—
37	#88123	—	4	2	no	—
38	C₁₃×#107	—	2	4	no	—
39	C₁₃×#107	—	2	2	no	—
40	C₁₃×#107	C₂³	1	4	yes	—
41	C₄×C₈×C₁₃	D₄	1	2	yes	—
42	C₄×C₈×C₁₃	C₂³	1	2	yes	—
43	C₂×#6090	—	2	4	no	—
44	C₂×#6090	C₂³	1	4	yes	—
45	C₂×#2241	—	13	1	no	maximal, Sylow
46	C₂×Q₈×C₁₃	—	4	4	no	—
47	C₂×Q₈×C₁₃	—	8	4	no	—
48	C₂²×C₄×C₁₃	—	4	2	no	—
49	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
50	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
51	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
52	C₂²×Dic₁₃	—	4	2	no	—
53	C₂×Dic₂₆	—	2	4	no	—
54	C₂×Dic₂₆	—	4	4	no	—
55	C₂×Dic₂₆	—	4	4	no	—
56	C₂×Dic₂₆	—	4	2	no	—
57	C₂×C₈×C₁₃	SD₁₆	1	4	yes	—
58	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
59	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
60	C₂×C₈×C₁₃	#41	1	4	yes	—
61	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
62	C₁₃×C₄⋊C₄	—	2	4	no	—
63	C₁₃×C₄⋊C₄	—	4	2	no	—
64	C₁₃×C₄⋊C₄	—	4	4	no	—
65	C₄²×C₁₃	D₈	1	2	yes	—
66	C₄²×C₁₃	C₂×D₄	1	2	yes	—
67	C₄⋊Dic₁₃	—	4	4	no	—
68	C₄⋊Dic₁₃	—	4	4	no	—
69	Dic₅₂	—	2	8	no	—
70	Dic₅₂	—	4	4	no	—
71	Dic₅₂	—	4	8	no	—
72	#6090	—	2	4	no	—
73	C₂×#500	D₁₃	1	1	yes	characteristic
74	C₂×#494	—	13	1	no	—
75	#2241	—	13	8	no	—
76	C₂×#358	—	13	4	no	—
77	C₂×C₄×C₁₆	—	13	1	no	—
78	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
79	Q₈×C₁₃	—	8	8	no	—
80	C₂×C₄×C₁₃	—	4	4	no	—
81	C₂×C₄×C₁₃	—	8	4	no	—
82	C₂×C₄×C₁₃	SD₃₂	1	4	yes	—
83	C₂×C₄×C₁₃	Q₃₂	1	4	yes	—
84	C₂×C₄×C₁₃	#124	1	2	yes	—
85	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
86	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
87	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
88	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
89	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
90	C₂×Dic₁₃	—	4	4	no	—
91	C₂×Dic₁₃	—	8	4	no	—
92	Dic₂₆	—	4	4	no	—
93	Dic₂₆	—	4	4	no	—
94	Dic₂₆	—	8	4	no	—
95	C₈×C₁₃	#124	1	2	yes	—
96	C₈×C₁₃	C₂×SD₁₆	1	4	yes	—
97	C₈×C₁₃	C₂×#41	1	2	yes	—
98	C₂²×Q₁₆	—	13	2	no	—
99	C₂²×Q₁₆	—	26	1	no	—
100	C₂×C₄⋊Q₈	—	2	1	no	—
101	C₂×C₄⋊Q₈	—	26	1	no	—
102	C₂²×C₁₆	—	13	2	no	—
103	#500	—	2	2	no	—
104	#500	C₂×D₁₃	1	4	yes	—
105	#494	—	13	4	no	—
106	#494	—	26	2	no	—
107	C₂×#107	—	2	1	no	—
108	C₂×#107	C₂×D₁₃	1	2	yes	—
109	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
110	#358	—	13	16	no	—
111	C₄×C₁₆	—	13	4	no	—
112	C₂²×C₁₃	#486	1	2	yes	—
113	C₂²×C₁₃	C₂×SD₃₂	1	2	yes	—
114	C₂²×C₁₃	C₂×Q₃₂	1	2	yes	—
115	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
116	C₄×C₁₃	—	8	4	no	—
117	C₄×C₁₃	#486	1	2	yes	—
118	C₄×C₁₃	C₂×SD₃₂	1	4	yes	—
119	C₄×C₁₃	C₂×Q₃₂	1	4	yes	—
120	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
121	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
122	Dic₁₃	—	8	4	no	—
123	C₂²×Q₈	—	4	1	no	—
124	C₂²×Q₈	—	26	2	no	—
125	C₂×Q₁₆	—	13	4	no	—
126	C₂×Q₁₆	—	26	8	no	—
127	C₂×Q₁₆	—	26	2	no	—
128	C₂×Q₁₆	—	26	4	no	—
129	C₂×Q₁₆	—	52	4	no	—
130	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
131	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
132	C₄⋊Q₈	—	2	4	no	—
133	C₄⋊Q₈	—	4	2	no	—
134	C₄⋊Q₈	—	26	4	no	—
135	C₄⋊Q₈	—	52	2	no	—
136	C₂×C₄⋊C₄	—	2	2	no	—
137	C₂×C₄⋊C₄	—	4	1	no	—
138	C₂×C₄⋊C₄	—	52	1	no	—
139	C₂×C₄⋊C₄	—	52	1	no	—
140	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
141	C₂×C₁₆	—	13	4	no	—
142	C₂×C₁₆	—	26	4	no	—
143	#107	—	2	4	no	—
144	#107	—	2	2	no	—
145	#107	C₂²×D₁₃	1	4	yes	—
146	C₄×C₈	C₂²⋊D₁₃	1	2	yes	—
147	C₄×C₈	C₂²×D₁₃	1	2	yes	—
148	C₂×C₁₃	#2241	1	4	yes	complemented
149	C₂×C₁₃	C₂×#486	1	1	yes	characteristic
150	C₂×C₁₃	C₂²×SD₃₂	1	1	yes	characteristic
151	C₂×C₁₃	C₂²×Q₃₂	1	1	yes	characteristic
152	C₂×Q₈	—	4	4	no	—
153	C₂×Q₈	—	8	4	no	—
154	C₂×Q₈	—	26	4	no	—
155	C₂×Q₈	—	52	2	no	—
156	C₂×Q₈	—	52	4	no	—
157	C₂×Q₈	—	52	4	no	—
158	C₂²×C₄	—	4	2	no	—
159	C₂²×C₄	—	52	2	no	—
160	C₂²×C₄	#6104	1	1	yes	characteristic
161	C₂²×C₄	#6104	1	1	yes	characteristic
162	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
163	Q₁₆	—	26	8	no	—
164	Q₁₆	—	52	8	no	—
165	Q₁₆	—	52	4	no	—
166	C₂×C₈	#6106	1	4	yes	—
167	C₂×C₈	#6131	1	4	yes	—
168	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
169	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
170	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
171	C₄⋊C₄	—	2	4	no	—
172	C₄⋊C₄	—	4	2	no	—
173	C₄⋊C₄	—	4	4	no	—
174	C₄⋊C₄	—	52	4	no	—
175	C₄⋊C₄	—	52	4	no	—
176	C₄²	#6104	1	2	yes	—
177	C₄²	C₂×C₂²⋊D₁₃	1	2	yes	—
178	C₁₆	—	26	4	no	—
179	C₁₃	C₂×#2241	1	1	yes	characteristic, complemented, Sylow
180	C₂³	C₂×#6104	1	1	yes	characteristic
181	Q₈	—	8	8	no	—
182	Q₈	—	52	4	no	—
183	Q₈	—	52	4	no	—
184	Q₈	—	104	4	no	—
185	C₂×C₄	—	4	4	no	—
186	C₂×C₄	—	8	4	no	—
187	C₂×C₄	—	52	4	no	—
188	C₂×C₄	—	104	4	no	—
189	C₂×C₄	#88067	1	4	yes	—
190	C₂×C₄	#88069	1	4	yes	—
191	C₂×C₄	C₂×#6104	1	1	yes	characteristic
192	C₂×C₄	C₂×#6104	1	2	yes	—
193	C₂×C₄	C₂×#6104	1	2	yes	—
194	C₂×C₄	C₂×#6106	1	2	yes	—
195	C₂×C₄	#88201	1	2	yes	—
196	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
197	C₈	C₂×#6106	1	4	yes	—
198	C₈	#88201	1	2	yes	—
199	C₈	C₂×#6131	1	2	yes	—
200	C₂²	#11718749	1	2	yes	—
201	C₂²	C₂×#88067	1	2	yes	—
202	C₂²	C₂×#88069	1	2	yes	—
203	C₂²	C₂²×#6104	1	1	yes	characteristic
204	C₄	—	8	4	no	—
205	C₄	—	104	4	no	—
206	C₄	#11718749	1	2	yes	—
207	C₄	C₂×#88067	1	4	yes	—
208	C₄	C₂×#88069	1	4	yes	—
209	C₄	C₂²×#6106	1	1	yes	characteristic
210	C₄	C₂×#88201	1	1	yes	characteristic
211	C₂	#13117065	1	4	yes	direct product factor
212	C₂	C₂×#11718749	1	1	yes	characteristic
213	C₂	C₂²×#88067	1	1	yes	characteristic
214	C₂	C₂²×#88069	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#6104
commutator, cosocle	C₂×C₈×C₁₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂×C₁₃×#500	C₂
socle, prime radical	C₂³×C₁₃	C₂×D₈
hypercenter	C₂×#500	D₁₃
hypocenter	C₁₃	C₂×#2241
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#500

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. #13117065	C₂	direct (N × H)
148. C₂×C₁₃	#2241	semidirect
179. C₁₃	C₂×#2241	semidirect
211. C₂	#13117065	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#11718360	2
#13117065	2
C₂×#11718084	2
C₂×C₄×#6090	2
C₂×C₁₃×#500	2
C₂×#2241	13

Subgroups — C2×#13117065 #16018209

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13117065 #16018209